A232113 a(n) is the Manhattan distance between n and 2*n in a square spiral of positive integers with 1 at the center.

1, 2, 3, 2, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 11, 8, 11, 12, 13, 12, 9, 10, 13, 16, 15, 12, 9, 12, 15, 16, 15, 12, 9, 12, 15, 14, 13, 12, 11, 12, 13, 12, 11, 10, 9, 10, 11, 10, 9, 8, 7, 8, 9

Offset

1,2

Comments

Spiral begins:

.

49 26--27--28--29--30--31

| | |

48 25 10--11--12--13 32

| | | | |

47 24 9 2---3 14 33

| | | | | | |

46 23 8 1 4 15 34

| | | | | |

45 22 7---6---5 16 35

| | | |

44 21--20--19--18--17 36

| |

43--42--41--40--39--38--37

.

Numbers n such that a(n)^2=n: 1, 4, 16, 625, 20736, 707281, 24010000, 815730721, ...; that is, 1, 4, 2^4, 5^4, 12^4, 29^4, 70^4, 169^4, ... (cf. Pell numbers: A000129).

Links

Table of n, a(n) for n=1..79.

Crossrefs

Cf. A000129, A214526, A232114, A232115.

Sequence in context: A278327 A067316 A210221 * A216475 A267807 A127433

Adjacent sequences: A232110 A232111 A232112 * A232114 A232115 A232116

Keyword

nonn

Author

Alex Ratushnyak, Nov 19 2013

Status

approved